Problem: Simplify the following expression: $r = \dfrac{4p}{3} + \dfrac{p}{7}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $3$ and $7$ $\lcm(3, 7) = 21$ $ r = \dfrac{7}{7} \cdot \dfrac{4p}{3} + \dfrac{3}{3} \cdot \dfrac{p}{7} $ $r = \dfrac{28p}{21} + \dfrac{3p}{21}$ $r = \dfrac{28p +3p}{21}$ $r = \dfrac{31p}{21}$